THE TOPP-LEONE WEIBULL DISTRIBUTION: ITS PROPERTIES AND APPLICATION TO LIFETIME DATA

Abstract

Lifetime distributions are statistical models used for analyzing real life problems based on survival time. Many statistical distributions have been proposed to model lifetime data and the one parameter Topp-Leone distribution is one of such distributions. Although, the distribution is one of the simplest distributions that exhibits a bathtub hazard rate property, but being a single parameter defined on a unit interval, its flexibility is limited in handling lifetime data sets. In this thesis, a new generalization of the Topp-Leone distribution called, the ToppLeone Weibull Distribution (TLWD) is introduced. Some of the mathematical properties of the proposed distribution are derived, and the maximum likelihood estimation method was adopted in estimating the parameters of the proposed distribution. An application of the proposed distribution alongside with some well-known distributions belonging to the Topp-Leone generated family of distributions to two real lifetime data sets reveals that the proposed distribution exhibits more flexibility in modeling lifetime data based on some comparison criteria such as maximized loglikelihood, Akaike Information Criterion, Kolmogorov-Smirnov test statistic (K − S) and Anderson Darling test statistic (A * ) and Crammer-von Mises test statistic (W* ).